H2MV (v1.0): global physically constrained deep learning water cycle model with vegetation

Abstract. The proposed hybrid hydrological model with vegetation (H2MV) uses dynamic meteorology and static features as input to a long short-term memory (LSTM) to model uncertain parameters of process formulations that govern water fluxes and states. In the hydrological model, vegetation states are represented by the fraction of absorbed photosynthetically active radiation (fAPAR), and soil storage capacity (SMmax⁡), which depends on effective rooting depth besides soil properties. SMmax⁡ and fAPAR are both learned and predicted by the neural networks directly. These parameters have an explicit role to model soil moisture (SM) storage and the partitioning of evapotranspiration (ET). The model is optimized concurrently against global observations and observation-based data of terrestrial water storage (TWS) anomalies, fAPAR, snow water equivalent (SWE), ET, and gridded runoff in a 10-fold cross-validation (CV) setup. To this end, we infer where the model is under-constrained such that different processes could explain the observational constraints in the model due to equifinality. The model reproduces the observed patterns of global hydrological components and fAPAR, while emergent patterns of runoff ratio, evaporative fraction, and the ratio of transpiration to ET are consistent with our current understanding. Despite robustly predicted temporal patterns of TWS anomalies, we found that the mean soil moisture state is not well constrained, causing uncertainty in mean TWS. This emphasizes the importance of SMmax⁡ and the necessity for associated enhanced constraints. The proposed model is open-source and has a highly flexible and modular structure to facilitate future integration of carbon and energy cycles, advancing toward a hybrid land surface model.